Kinetic entropy for the layer-averaged hydrostatic Navier-Stokes equations

Emmanuel Audusse (1) , Marie-Odile Bristeau (2, 3) , Jacques Sainte-Marie (2, 3)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 ANGE - Numerical Analysis, Geophysics and Ecology
3 Cerema Direction Eau Mer et Fleuves - Centre d'Etudes et d'Expertise sur les Risques, l'Environnement, la Mobilité et l'Aménagement - Direction Eau Mer et Fleuves

We are interested in the numerical approximation of the hydrostatic free surface incompressible Navier-Stokes equations. By using a layer-averaged version of the equations, we are able to extend previous results obtained for shallow water system. We derive a vertically implicit / horizontally explicit finite volume kinetic scheme that ensures the positivity of the approximated water depth, the well-balancing and a fully discrete energy inequality.

Mots clés: kinetic solver; finite volumes; Incompressible Euler and Navier-Stokes sytems; hydrostatic reconstruction; IMEX scheme; free surface flows; layer-averaged model; discrete entropy inequality

Domaines: Analyse numérique [math.NA]

Emmanuel Audusse, Marie-Odile Bristeau, Jacques Sainte-Marie. Kinetic entropy for the layer-averaged hydrostatic Navier-Stokes equations. 2017. ⟨hal-01583511v2⟩